Solve 1/2-5/6x<2

$$\frac { 1 } { 2 } - \frac { 5 } { 6 } x < 2$$

Solve for x

$$x>-\frac{9}{5}$$

Solution Steps

Subtract \frac{1}{2} from both sides.

$$-\frac{5}{6}x<2-\frac{1}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$-\frac{5}{6}x<\frac{4}{2}-\frac{1}{2}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{6}x<\frac{4-1}{2}$$

Subtract 1 from 4 to get 3.

$$-\frac{5}{6}x<\frac{3}{2}$$

Multiply both sides by -\frac{6}{5}, the reciprocal of -\frac{5}{6}. Since -\frac{5}{6} is negative, the inequality direction is changed.

$$x>\frac{3}{2}\left(-\frac{6}{5}\right)$$

Multiply \frac{3}{2} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{3\left(-6\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{3\left(-6\right)}{2\times 5}.

$$x>\frac{-18}{10}$$

Reduce the fraction \frac{-18}{10} to lowest terms by extracting and canceling out 2.

$$x>-\frac{9}{5}$$